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LTI-Discrete time System, Frequency Response, Fourier Transforms, Difference Equation

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    An LTI discrete-time system has frequency response given by
    33bz3py.jpg

    (a) Use one of the above forms of the frequency response to obtain an equation for the
    impulse response h[n] of the system.

    (b) From the frequency response, determine the difference equation that is satisfied by
    the input x[n] and the output y[n] of the system.

    (c) If the input to this system is
    x[n]=4+2cos(won) for oo<n<oo,
    for what value of wo will the output be of the form
    y[n] =A constant
    for -00 < n < oo? What is the constant A?


    2. The attempt at a solution
    (a) i found to be
    h[n] = (0.8)^n u[n] + (0.8)^n-2 u[n-2]

    Can anyone help me with the rest of the two parts?
     
  2. jcsd
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